一维立方-五次方薛定谔方程的小驻留孤波的渐近稳定性

IF 2.6 1区数学 Q1 MATHEMATICS

Inventiones mathematicae Pub Date : 2024-05-28 DOI:10.1007/s00222-024-01270-4

Yvan Martel

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引用次数: 0

摘要

对于在一个空间维度上具有三次-五次、聚焦-聚焦非线性的薛定谔方程，本文证明了小驻留孤波族在能量空间均匀扰动下的局部渐近完备性。该模型是可积分立方薛定谔方程小解的扰动模型，围绕小孤波的线性化方程有一个内模，其对动力学的贡献由费米黄金法则处理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation

For the Schrödinger equation with a cubic-quintic, focusing-focusing nonlinearity in one space dimension, this article proves the local asymptotic completeness of the family of small standing solitary waves under even perturbations in the energy space. For this model, perturbative of the integrable cubic Schrödinger equation for small solutions, the linearized equation around a small solitary wave has an internal mode, whose contribution to the dynamics is handled by the Fermi golden rule.

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来源期刊

Inventiones mathematicae 数学-数学

CiteScore

5.60

自引率

3.20%

发文量

审稿时长

12 months

期刊介绍： This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author(s).